Bohner, M.; Saker, S. H. Oscillation criteria for perturbed nonlinear dynamic equations. (English) Zbl 1112.34019 Math. Comput. Modelling 40, No. 3-4, 249-260 (2004). Summary: We discuss the oscillatory behavior of a certain nonlinear perturbed dynamic equation on time scales. We establish some new oscillation criteria for such dynamic equations and supply examples. Cited in 25 Documents MSC: 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 39A11 Stability of difference equations (MSC2000) Keywords:Oscillation; Second-order nonlinear dynamic equation; Time scale; Riccati transformation technique; Positive solution PDFBibTeX XMLCite \textit{M. Bohner} and \textit{S. H. Saker}, Math. Comput. Modelling 40, No. 3--4, 249--260 (2004; Zbl 1112.34019) Full Text: DOI References: [1] Hilger, S., Analysis on measure chains—A unified approach to continuous and discrete calculus, Results Math., 18, 18-56 (1990) · Zbl 0722.39001 [2] Bohner, M.; Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (2001), Birkhäuser: Birkhäuser New York, NY · Zbl 0978.39001 [3] Bohner, M.; Peterson, A., Advances in Dynamic Equations on Time Scales (2003), Birkhäuser: Birkhäuser Boston · Zbl 1025.34001 [4] Agarwal, R. P.; Grace, S. R.; O’Regan, D., Oscillation Theory for Difference and Functional Differential Equations (2000), Kluwer Academic: Kluwer Academic Boston · Zbl 0969.34062 [5] Akin, E.; Erbe, L.; Kaymakgalan, B.; Peterson, A., Oscillation results for a dynamic equation on a time scale, J. Differ. Equations Appl., 7, 6, 793-810 (2001) · Zbl 1002.39024 [6] Bohner, M.; Dosly, O.; Kratz, W., An oscillation theorem for discrete eigenvalue problems, Rocky Mountain J. Math., 33, 4, 1233-1260 (2003) · Zbl 1060.39003 [7] Bohner, M.; Saker, S. H., Oscillation of second order nonlinear dynamic equations on time scales, Rocky Mountain J. Math., 34, 4, 1239-1254 (2004) · Zbl 1075.34028 [8] Došlý, O.; Hilger, S., A necessary and sufficient condition for oscillation of the Sturm-Liouville dynamic equation on time scales, (Agarwal, R. P.; Bohner, M.; O’Regan, D., Dynamic Equations on Time Scales. Dynamic Equations on Time Scales, J. Comput. Appl. Math., 141 (2002)), 147-158, a Special Issue of · Zbl 1009.34033 [9] Erbe, L.; Peterson, A., Positive solutions for a nonlinear differential equation on a measure chain, Mathl. Comput. Modelling, 32, 5/6, 571-585 (2000) · Zbl 0963.34020 [10] Erbe, L.; Peterson, A., Riccati equations on a measure chain, (Ladde, G. S.; Medhin, N. G.; Sambandham, M., Proceedings of Dynamic Systems and Applications, Atlanta, GA, Volume 3 (2001), Dynamic Publishers: Dynamic Publishers Dordrecht), 193-199 · Zbl 1008.34006 [11] Erbe, L.; Peterson, A., Oscillation criteria for second order matrix dynamic equations on a time scale, (Agarwal, R. P.; Bohner, M.; O’Regan, D., Dynamic Equations on Time Scales. Dynamic Equations on Time Scales, J. Comput. Appl. Math., 141 (2002)), 169-185, a Special Issue of · Zbl 1017.34030 [12] Erbe, L.; Peterson, A.; Saker, S. H., Oscillation criteria for second-order nonlinear dynamic equations on time scales, J. London Math. Soc., 67, 3, 701-714 (2003) · Zbl 1050.34042 [13] Guseinov, G. Sh.; Kaymakçalan, B., On a disconjugacy criterion for second order dynamic equations on time scales, (Agarwal, R. P.; Bohner, M.; O’Regan, D., Dynamic Equations on Time Scales. Dynamic Equations on Time Scales, J. Comput. Appl. Math., 141 (2002)), 187-196, a Special Issue of · Zbl 1014.34023 [14] Bohner, M.; Guseinov, G. Sh., Improper integrals on time scales, Dynam. Systems Appl., 12, 1/2, 45-66 (2003) · Zbl 1058.39011 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.